Method for production of a mechanical resonator with a planar monolitiiic vibrating structure machined in a crystalline material and resonator produced thus

ABSTRACT

The invention relates to the production of a mechanical resonator with a planar monolithic vibrating structure machine in a crystalline material. Where the material is trigonal (1), trigonal (2) or hexagonal in structure, said material is cut in the [001] plane or, where said material is cubic in structure, said material is cut in the [111] plane and the vibration mode of order 2 is used. Where the material is tetragonal (1) or tetragonal (2) or hexagonal said material is cut in the [001] plane or where said material is cubic in structure said material is cut in the [001], [100], or [010] plane and the vibration mode of order 3 is used. The resonator thus has a natural material frequency isotropy (Δf m =0).

FIELD OF THE INVENTION

The present invention relates to improvements made in the field ofgyroscopic devices based on mechanical resonators with a planarmonolithic vibrating structure machined in a crystalline material.

DESCRIPTION OF THE PRIOR ART

Gyroscopic devices are devices for measuring a speed of rotation or anangle of rotation about one or more particular axes.

At the present time, there are many techniques used for producinggyroscopic devices, but currently there is a need to have very compactdevices (with a size of less than a few cubic centimeters) that can beachieved in high volume for low cost, that can withstand suddenaccelerations of high level, and are capable of delivering accuratemeasurements within a wide range of rotation speeds. Among potentialfields of application for such devices, mention may especially be madeof the navigation and guiding of small spin-controlled missiles (forexample short-range antitank missiles) or spin-controlled munitions(shells or mortars), that is to say projectiles rotating about the rollaxis at a high permanent speed of rotation, typically a few revolutionsper second in the case of spin-controlled missiles or fin-controlledprojectiles, and a few hundred revolutions per second in the case ofgyro-controlled projectiles.

To meet this requirement, the technology of vibrating gyroscopes,combined with fabrication of micromachined structures, is particularlysuitable. However, although several formulations have emerged andreached a relatively advanced stage of development andindustrialization, none of them allows the problem posed by theabovementioned applications to be correctly solved, for which a rotationmeasurement about the roll axis is necessary. This inability of suchformulations to correctly meet the needs stems from the combination oftwo causes:

-   -   the first cause is that they are intrinsically suited to        gyrometer-type feedback control (measurement of angular        velocity);    -   the second cause is that the dynamics of the speed of rotation        about the roll axis are too fast for gyrometric feedback control        to offer sufficient precision and/or result in saturating the        sensor electronics used.

Consequently, it is known that the only possible general solution to theproblem posed consists in using the devices intrinsically adapted togyroscopic feedback control (measurement of the angle of rotation).Furthermore, as specified in document FR 2 756 375, the gyroscopicfeedback control of a vibrating mechanical resonator placed along theroll axis of a carrier allows high scale-factor precision to beobtained. In combination with resonators feedback-controlled ingyrometer mode about the transverse axes of the carrier, it is thuspossible to produce a high-performance system for which the bias errorsof the transverse resonators cancel out over one revolution of thecarrier about its roll axis.

In the case of devices based on vibrating gyroscope technology, thecondition of optimum gyroscopic feedback control involves searching forstructures whose frequency anisotropy between the two useful modescoupled through the effect of Coriolis forces is intrinsically zero. Thefrequency anisotropy may be decomposed into three main terms:Δf=Δf _(m) +Δf _(g) +Δf _(s)where

-   Δf is the overall frequency anisotropy,-   Δf_(m) is the frequency anisotropy introduced by the material of the    resonator,-   Δf_(g) is the frequency anisotropy introduced by the geometry of the    resonator and-   Δf_(s) is the frequency anisotropy introduced by the suspension or    attachment of the resonator.

Other terms could be added, such as for example the anisotropiesintroduced by the electronics used, but these terms are assumed to be ofsecond order compared with the terms mentioned here.

Thus, in order for the overall frequency anisotropy Δf to be zero, it issufficient for the three components Δf_(m), Δf_(g) and Δf_(s) all to bezero. Other sufficient conditions are possible, but they necessarilyimply compensations between the Δf_(m) and/or Δf_(g) and/or Δf_(s)components, which ends up increasing the complexity of the definition ofthe structure of the resonator and makes this structure particularlysensitive to the variations of any parameter. It therefore seemsfundamental to seek structures for which each term Δf_(m), Δf_(g) andΔf_(s) is zero. However, it is found that the design approach usuallyadopted consists, in the case of micromachined resonator structures, intaking into account only the geometrical aspects, whereas it is just asfundamental to consider the constituent material of the resonatorthrough its intrinsic symmetries or its symmetries resulting from thecut plane in which the wafer supporting the resonator structure will becut.

By way of an example illustrating what has just been explained, theknown example of a vibrating ring whose geometry is perfectly suited toobtaining gyroscopic feedback control may be considered. By producingthis structure in a silicon wafer (by wet etching) cut in the [001]plane and by using the two plane modes of elliptical deformation asprincipal mode and as secondary mode, Δf_(g)=0 is of course obtained,but Δf_(m) is very much greater than 1 Hz. In practice, for a ring witha mean frequency of 400 Hz, having a diameter of 5 mm and a thickness of100 μm, Δf_(m)=250 Hz is obtained, so that in the end, by neglecting thefrequency anisotropy introduced by the attachment or other elements, anoverall frequency anisotropy Δf of about 250 Hz is obtained. This resultis incompatible with effective gyroscopic feedback control and clearlyillustrates the problem raised in the case of resonators obtained usingmicroelectronics technologies.

This is because micromachined resonator structures use, as supportmaterials, crystalline materials that are naturally anisotropic andconsequently lend themselves particularly well to micromachining bychemical etching, as is carried out for collective processes inmicroelectronics. However, offset against the advantage associated withthe collective aspect of the machining operations there is the majordrawback of the anisotropy of the material. This anisotropy, when noselection rule for the symmetries of the material consistent with thesymmetry of the modes used is respected, irremediably results in anonzero term Δf_(m).

DETAILED DESCRIPTION OF THE INVENTION

The object of the invention is therefore to propose a technologicalsolution (method and device) which achieves, with certainty, frequencyisotropy introduced by the crystalline material from which the vibratingresonator with a planar structure is cut, it being understood that thepresent invention is aimed solely at providing the means for obtainingfrequency isotropy introduced by the material (Δf_(m)=0) and that theproblems of obtaining frequency isotropies due to the geometry (Δf_(g))and to the suspension (Δf_(s)) are to be solved elsewhere for thepurpose of obtaining overall frequency isotropy (Δf=0) capable ofconstituting an intrinsically gyroscopic device (see for exampledocument FR 01/02498).

It should be understood that, if the material of the resonator isisotropic, then the intrinsic pulses of the two kth-order modes becomeequal, this being so whatever k, namely ω₁=ω_(2=ω.)

Moreover, the shapes of the two kth-order eigenmodes are identical byrotation of the reference frame through an angle of π/2k. Thus, the2nd-order modes of the vibrating ring correspond to elliptical shapesoffset one with respect to the other by an angle of π/4=45°. Likewise,the 3rd-order modes of the vibrating ring correspond to trilobate shapesoffset one with respect to another by an angle of π/6=30°.

The cut plane of the crystalline material is defined by the position ofits normal vector {right arrow over (V)}, which is itself defined by itscoordinates [x, y, z] in an orthonormal coordinate system Oex, ey, ez.Thus, the sole datum of the three information items [x, y, z] allows thenormal vector {right arrow over (V)}, and therefore the cut plane, to beuniquely defined. For example, the [001] datum gives the coordinates ofthe normal vector and the plane is parallel to the (ex, ey) plane.

Moreover, it is known that currently known crystalline materials can bedivided up into 32 classes distributed in nine families from thestandpoint of the representation of rigidity and flexibility matrices:mention may especially be made of the tetragonal (1), tetragonal (2),trigonal (1), trigonal (2), hexagonal and cubic families.

Finally, it should be pointed out that only the vibration modes of orderk=2 and k=3 of the vibrating resonators may at the present time beexploited in a practical fashion, whereas the exploitation of vibrationmodes of higher order (k=4, 5, etc.) would require very complexelectronics to be used (increasing the number of excitation/detectionelectrodes would be incompatible with production of a gyroscopic deviceof small, or even very small, size).

Admittedly, document WO 01/55675 mentions, just for a silicon crystal,the possibility of a 2nd-order vibration mode with a silicon crystal cutin the [111] plane and a 3rd-order mode with a silicon crystal cut inthe [100] plane. However, this is one specific item of information thatdoes not provide a person skilled in the art with any indication, in thecase of 2nd- and 3rd order vibrations, as regards the other possible cutplanes for silicon, or as regards possible cut planes for othercrystalline materials with a cubic structure, or more generally asregards possible cut planes for other crystalline materials.

Having mentioned this, the invention, in a first of its aspects,proposes a method for producing a mechanical resonator with a planarmonolithic vibrating structure machined in a crystalline material,characterized in that:

-   -   when the crystalline material is chosen from crystalline        materials of trigonal (1) or trigonal (2) or hexagonal        structure, this material is cut in the [001] plane or, when it        is chosen from materials of cubic structure (silicon excluded),        it is cut in the [111] plane, and the 2nd-order vibration mode        is then used, or else    -   when the crystalline material is chosen from crystalline        materials of tetragonal (1) or tetragonal (2) or hexagonal        structure, this material is cut in the [001] plane, or, when it        is chosen from materials of cubic structure, it is cut in the        [001] or [100] plane (silicon excluded) or [010] plane, and the        3rd-order vibration mode is then used,        whereby the resonator exhibits natural material-based frequency        isotropy (Δf_(m)=0).

These features may be summarized as follows:

Of course, the use of the provisions presented may accompany aconstruction of axisymmetric structure, resulting in geometry-basedisotropy Δf_(g)=0.

According to a second of its aspects, the invention proposes amechanical resonator with a planar monolithic vibrating structuremachined in a crystalline material, characterized in that, for theresonator to exhibit material-based frequency isotropy (Δf_(m)=0), thecrystalline material is chosen from the following:

-   -   a) a crystalline material of tetragonal (1) or tetragonal (2)        structure cut in the [001] plane, the resonator then exhibiting        material-based frequency isotropy in the 3rd-order vibration        mode;    -   b) a crystalline material of trigonal (1) or trigonal (2)        structure cut in the [001] plane, the resonator then exhibiting        material-based frequency isotropy in the 2nd-order vibration        mode;    -   c) a crystalline material of hexagonal structure cut in the        [001] plane, the resonator then exhibiting material-based        frequency isotropy in both the 2nd- and 3rd-order vibration        modes; and    -   d) a crystalline material of cubic structure        -   cut in the [111] plane (silicon excluded), the resonator            then exhibiting material-based frequency isotropy in the            2nd-order vibration mode or        -   cut in the [001], [100] (silicon excluded) or [010] planes,            the resonator then exhibiting material-based frequency            isotropy in the 3rd-order vibration mode.

As a consequence of this, a resonator produced in accordance with theinvention by a suitable choice of the constituent crystalline material,of the cut plane of said crystalline material and of the kth-ordervibration mode exhibits material-based frequency isotropy (Δf_(m)=0)and, provided that overall frequency isotropy Δf=0 is obtained (forexample with Δf_(g)=0 and Δf_(s)=0, or with Δf_(g)+Δf_(s)=0) such aresonator may constitute the core for a gyroscopic device of optimumdesign.

1. A method for producing a mechanical resonator with a planarmonolithic vibrating structure machined in a crystalline material,characterized in that: when the crystalline material is chosen fromcrystalline materials of trigonal (1) or trigonal (2) or hexagonalstructure, this material is cut in the [001] plane or, when it is chosenfrom materials of cubic structure (silicon excluded), it is cut in the[111] plane, and the 2nd-order vibration mode is then used, or else whenthe crystalline material is chosen from crystalline materials oftetragonal (1) or tetragonal (2) or hexagonal structure, this materialis cut in the [001] plane, or, when it is chosen from materials of cubicstructure, it is cut in the [001] or [100] plane (silicon excluded) or[010] plane, and the 3rd-order vibration mode is then used, whereby theresonator exhibits natural material-based frequency isotropy (Δf_(m)=0).2. A mechanical resonator with a planar monolithic vibrating structuremachined in a crystalline material, characterized in that, for theresonator to exhibit material-based frequency isotropy (Δf_(m)=0), thecrystalline material is chosen from the following: a) a crystallinematerial of tetragonal (1) or tetragonal (2) structure cut in the [001]plane, the resonator then exhibiting material-based frequency isotropyin the 3rd-order vibration mode; b) a crystalline material of trigonal(1) or trigonal (2) structure cut in the [001] plane, the resonator thenexhibiting material-based frequency isotropy in the 2nd-order vibrationmode; c) a crystalline material of hexagonal structure cut in the [001]plane, the resonator then exhibiting material-based frequency isotropyin both the 2nd- and 3rd-order vibration modes; and d) a crystallinematerial of cubic structure cut in the [111] plane (silicon excluded),the resonator then exhibiting material-based frequency isotropy in the2nd-order vibration mode or cut in the [001], [100] (silicon excluded)or [010] planes, the resonator then exhibiting material-based frequencyisotropy in the 3rd-order vibration mode.